A general quantified Ingham-Karamata Tauberian theorem

2024/11/06 by Gregory Debruyne, Debruyne, Gregory · 1 citation
Mathematics · #44A10 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Primary 40E05 #Secondary 11M45

paper · pdf · doi:10.48550/arxiv.2411.03809

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a general quantified Ingham-Karamata Tauberian theorem with a flexible one-sided Tauberian condition under several types of boundary behavior for the Laplace transform. Our results in particular improve a theorem by Stahn, removing a vexing restriction on the growth of the Laplace transform. Improving existing optimality results, we also show that the obtained quantified rate is optimal in almost all cases.

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• Optimal decay of semi-uniformly stable operator semigroups with empty spectrum

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